Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings

TL;DR

This paper introduces a supersymmetric Lagrangian for a nonlocal six-dimensional (2,0)-theory involving fixed-shape string-like objects called curvepoles, extending the understanding of (2,0)-theories and their relation to lower-dimensional gauge theories.

Contribution

It explicitly constructs a supersymmetric Lagrangian for an abelian curvepole (2,0)-theory with fixed-shape strings, a novel deformation of the free tensor multiplet.

Findings

Supersymmetry preserved up to quartic terms for planar curvepoles.

Provides a Lagrangian formulation for a nonlocal 6d theory involving fixed-shape strings.

Suggests the theory as a UV completion for certain 5d gauge theories.

Abstract

"Curvepole (2,0)-theory" is a deformation of the (2,0)-theory with nonlocal interactions. A "curvepole" is defined as a two-dimensional generalization of a dipole. It is an object of fixed two-dimensional shape whose boundary is a charged curve that interacts with a two-form gauge field. Curvepole theory was previously only defined indirectly via M-theory. Here we propose a supersymmetric Lagrangian, constructed explicitly up to quartic terms, for an "abelian" curvepole theory, which is an interacting deformation of the free (2,0) tensor mutliplet. This theory contains fields whose quanta are curvepoles (i.e., fixed-shape strings). Supersymmetry is preserved (at least up to quartic terms) if the shape of the curvepoles is (2d) planar. This nonlocal 6d QFT may also serve as a UV completion for certain (local) 5d gauge theories.